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Over-the-Air Modulation for RIS-assisted Symbiotic Radios: Design, Analysis, and Optimization

Hu Zhou, Ying-Chang Liang, Chau Yuen

TL;DR

This work tackles over-the-air modulation in RIS-assisted symbiotic radios by splitting the RIS phase-shift matrix into an assistance part and a transmission part, enabling simultaneous primary support and secondary transmission. The authors formalize a problem that maximizes secondary BER performance under a primary BER requirement controlled by an assistance factor $\delta$, and solve it via alternating optimization, SDR, and SCA, complemented by a low-complexity MRT-ZF beamforming structure. Key contributions include a BER performance framework with MED approximations, a tractable problem formulation P1, and both high- and low-complexity algorithms that balance primary and secondary reliability through the two-beamforming RIS design. Simulation results show a tunable BER tradeoff governed by $\delta$ and $N$, with the proposed scheme mitigating the BER floor and addressing detection ambiguity, thereby enhancing spectrum- and energy-sharing in RIS-enabled SR.

Abstract

In reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR), an RIS is exploited to assist the primary system and to simultaneously operate as a secondary transmitter by modulating its own information over the incident primary signal from the air. Such an operation is called over-the-air modulation. The existing modulation schemes such as on-off keying and binary phase-shift keying suffer from two problems for joint detection of the primary and secondary signals in RIS-assisted SR, i.e., one is the detection ambiguity problem when the direct link is blocked, and the other is the bit error rate (BER) error-floor problem when the direct link is weak. To address the two problems, we propose a novel modulation scheme by dividing the phase-shift matrix into two parts: one is the assistance beamforming matrix for assisting the primary system and the other is the transmission beamforming matrix for delivering the secondary signal. To optimize the assistance and transmission beamforming matrices, we first introduce an assistance factor that describes the performance requirement of the primary system and then formulate a problem to minimize the BER of the secondary system, while guaranteeing the BER requirement of the primary system controlled by the assistance factor. To solve this non-convex problem, we resort to the successive convex approximation technique to obtain a suboptimal solution. Furthermore, to draw more insights, we propose a low-complexity assistance-transmission beamforming structure by borrowing the idea from the classical maximum ratio transmission and zero forcing techniques. Finally, simulation results reveal an interesting tradeoff between the BER performance of the primary and secondary systems by adjusting the assistance factor.

Over-the-Air Modulation for RIS-assisted Symbiotic Radios: Design, Analysis, and Optimization

TL;DR

This work tackles over-the-air modulation in RIS-assisted symbiotic radios by splitting the RIS phase-shift matrix into an assistance part and a transmission part, enabling simultaneous primary support and secondary transmission. The authors formalize a problem that maximizes secondary BER performance under a primary BER requirement controlled by an assistance factor , and solve it via alternating optimization, SDR, and SCA, complemented by a low-complexity MRT-ZF beamforming structure. Key contributions include a BER performance framework with MED approximations, a tractable problem formulation P1, and both high- and low-complexity algorithms that balance primary and secondary reliability through the two-beamforming RIS design. Simulation results show a tunable BER tradeoff governed by and , with the proposed scheme mitigating the BER floor and addressing detection ambiguity, thereby enhancing spectrum- and energy-sharing in RIS-enabled SR.

Abstract

In reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR), an RIS is exploited to assist the primary system and to simultaneously operate as a secondary transmitter by modulating its own information over the incident primary signal from the air. Such an operation is called over-the-air modulation. The existing modulation schemes such as on-off keying and binary phase-shift keying suffer from two problems for joint detection of the primary and secondary signals in RIS-assisted SR, i.e., one is the detection ambiguity problem when the direct link is blocked, and the other is the bit error rate (BER) error-floor problem when the direct link is weak. To address the two problems, we propose a novel modulation scheme by dividing the phase-shift matrix into two parts: one is the assistance beamforming matrix for assisting the primary system and the other is the transmission beamforming matrix for delivering the secondary signal. To optimize the assistance and transmission beamforming matrices, we first introduce an assistance factor that describes the performance requirement of the primary system and then formulate a problem to minimize the BER of the secondary system, while guaranteeing the BER requirement of the primary system controlled by the assistance factor. To solve this non-convex problem, we resort to the successive convex approximation technique to obtain a suboptimal solution. Furthermore, to draw more insights, we propose a low-complexity assistance-transmission beamforming structure by borrowing the idea from the classical maximum ratio transmission and zero forcing techniques. Finally, simulation results reveal an interesting tradeoff between the BER performance of the primary and secondary systems by adjusting the assistance factor.
Paper Structure (29 sections, 2 theorems, 47 equations, 9 figures, 1 algorithm)

This paper contains 29 sections, 2 theorems, 47 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Over-the-Air Modulation
  4. Received Signal Model
  5. Receiver Design
  6. Detection at the PU
  7. Receiver Design at the SU
  8. BER Performance Analysis
  9. BER Performance of the Primary System
  10. BER Performance of the Secondary System
  11. BER Approximation via Minimum Euclidean Distance
  12. Performance Limits of Existing Modulation Scheme
  13. Problem Formulation
  14. Proposed Algorithms
  15. Active Transmit Beamforming Optimization
  16. ...and 14 more sections

Key Result

Lemma 1

(Feasibility of problem P-ZF) P-ZF is feasible if and only if the following condition is satisfied where $\|\bm{f}_{p}\|_{\infty}=\max \limits_{n=1,\cdots,N} \{|f_{p,n}|\}$, $\|\bm{f}_{p}\|_{1}=\sum_{n=1}^{N}|f_{p,n}|$, and $f_{p,n}$ denotes the $n$-th element of $\bm{f}_{p}$.

Figures (9)

  • Figure 1: System model of RIS-assisted symbiotic radios.
  • Figure 2: Convergence behaviour for solving P1.
  • Figure 3: BER performance of primary and secondary systems, $P_s$ and $P_c$, versus the assistance factor, $\delta$.
  • Figure 4: Feasible probability for solving P1 versus the assistance factor, $\delta$, under different RIS design schemes.
  • Figure 5: BER performance of the primary system, $P_s$, versus the number of reflecting elements, $N$
  • ...and 4 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Proposition 1